Which set of numbers is always irrational?(1 point)
Responses
non-terminating, non-repeating decimals
non-terminating, non-repeating decimals
positive decimals
positive decimals
repeating decimals
repeating decimals
terminating decimals
non-terminating, non-repeating decimals
The diagonal of a square equals 2–√
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 70 feet on a side?(1 point)
To find the length from one corner to an opposite corner of a square park, we can use the formula:
diagonal length = (2–√) * side length
Given that the side length is 70 feet, we can substitute this value into the formula:
diagonal length = (2–√) * 70
Substituting the approximate value 1.4 for the square root of 2:
diagonal length ≈ (2–1.4) * 70
diagonal length ≈ 0.6 * 70
diagonal length ≈ 42 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 42 feet.
Four people have found the distance in kilometers across a small bridge using different methods. Their results are given in the table. Order the distances from least to greatest.
A. 5 1/2, 28, 5.5, 23/4
B. 28, 5 1/2, 5.5, 23/4
C. 28, 5.5, 23/4, 5 1/2
D. 23/4, 5.5, 28, 5 1/2
To order the distances from least to greatest, we need to convert all the distances into the same format.
Let's convert 5 1/2 to its decimal form. 5 1/2 is equal to 5.5.
Now, let's convert 23/4 to its decimal form. To do this, we divide 23 by 4, resulting in 5.75.
Now that all the distances are in decimal form, we can order them from least to greatest:
5.5, 5.75, 28
Therefore, the correct order is:
C. 28, 5.5, 23/4, 5 1/2
Using a number line, what whole number and rational number to the nearest half is 30 between? (1 point)
30 is between blank and blank
To determine the whole number and rational number to the nearest half that 30 is between, we can locate 30 on a number line:
0-------------------30-------------------60
We can see that 30 is exactly halfway between the whole numbers 0 and 60. However, since the question asks for the nearest half, we need to consider the rational numbers in increments of 0.5.
If we divide the space between 0 and 60 into increments of 0.5, we can determine the rational number to the nearest half that 30 is between:
0, 0.5, 1, 1.5, ... 28, 28.5, 29, 29.5, 30, 30.5, 31, 31.5, ..., 59, 59.5, 60
Therefore, the whole number and rational number to the nearest half that 30 is between is:
29 and 30.5
Using a number line, what whole number and rational to the nearest half is 68 between?
A. between 9 and 9.5
B. between 8.5 and 9
C. between 7.5 and 8
D. between 8 and 8.5
To determine the whole number and rational number to the nearest half that 68 is between, we can locate 68 on a number line:
0----------------------------68---------------------------100
We can see that 68 is closer to 68.5 than any other option given. Therefore, the correct answer is:
A. between 9 and 9.5
Using rational approximations, what is an inequality statement comparing 91 and 98? Enter greater, less, or equal
The inequality is: 91 blank 98